10=−4x+3x^2 solve

please help!

Step-by-step explanation:

Rearrange terms

1

0

=

−

4

+

3

2

10={\color{#c92786}{-4x+3x^{2}}}

10=−4x+3x2

1

0

=

3

2

−

4

10={\color{#c92786}{3x^{2}-4x}}

10=3x2−4x

2

Move terms to the left side

1

0

=

3

2

−

4

10=3x^{2}-4x

10=3x2−4x

1

0

−

(

3

2

−

4

)

=

0

10-\left(3x^{2}-4x\right)=0

10−(3x2−4x)=0

3

Distribute

1

0

−

(

3

2

−

4

)

=

0

10-\left(3x^{2}-4x\right)=0

10−(3x2−4x)=0

1

0

−

3

2

+

4

=

0

10-3x^{2}+4x=0

10−3x2+4x=0

4

Rearrange terms

1

0

−

3

2

+

4

=

0

10-3x^{2}+4x=0

10−3x2+4x=0

−

3

2

+

4

+

1

0

=

0

-3x^{2}+4x+10=0

−3x2+4x+10=0

5

Common factor

−

3

2

+

4

+

1

0

=

0

-3x^{2}+4x+10=0

−3x2+4x+10=0

−

(

3

2

−

4

−

1

0

)

=

0

-\left(3x^{2}-4x-10\right)=0

−(3x2−4x−10)=0

6

Divide both sides of the equation by the same term

−

(

3

2

−

4

−

1

0

)

=

0

-\left(3x^{2}-4x-10\right)=0

−(3x2−4x−10)=0

3

2

−

4

−

1

0

=

0

3x^{2}-4x-10=0

3x2−4x−10=0

7

Use the quadratic formula

=

−

±

2

−

4

√

2

x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c{2{\color{#c92786}{a}}}

x=2a−b±b2−4ac​​

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

3

2

−

4

−

1

0

=

0

3x^{2}-4x-10=0

3x2−4x−10=0

=

3

a={\color{#c92786}{3}}

a=3

=

−

4

b={\color{#e8710a}{-4}}

b=−4

=

−

1

0

c={\color{#129eaf}{-10}}

c=−10

=

−

(

−

4

)

±

(

−

4

)

2

−

4

⋅

3

(

−

1

0

)

√

2

⋅

3

x=\frac{-({\color{#e8710a}{-4}}) \pm \sqrt{({\color{#e8710a}{-4}})^{2}-4 \cdot {\color{#c92786}{3}}({\color{#129eaf}{-10}})}}{2 \cdot {\color{#c92786}{3}}}

x=2⋅3−(−4)±(−4)2−4⋅3(−10)​​

8

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Factorization

Factorization

Factorization

Evaluate the square root

Evaluate the square root

Multiply the numbers

Multiply the numbers

=

4

±

2

3

4

√

6

x=\frac{4 \pm 2\sqrt{34}}{6}

x=64±234​​

9

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

=

4

+

2

3

4

√

6

x=\frac{4+2\sqrt{34}}{6}

x=64+234​​

=

4

−

2

3

4

√

6

x=\frac{4-2\sqrt{34}}{6}

x=64−234​​

10

Solve

Rearrange and isolate the variable to find each solution

=

2

+

3

4

√

3

x=\frac{2+\sqrt{34}}{3}

x=32+34​​

=

2

−

3

4

√

3

x=\frac{2-\sqrt{34}}{3}

x=32−34​​

=

2

±

3

4

4.08%

step-by-step explanation: